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arXiv · 0912.0174

On the two dimensional Berwald-Landsberg problem

Ricardo Gallego Torrome
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Abstract

The Berwald-Landsberg problem is considered for two dimensional manifolds. We sketch the proof that there are not $\mathcal{C}^5$-regular $y$-global pure Landsberg surfaces. The method used consists on considerer the holonomy representation of the averaged Chern connection and then exhausting all the possible cases, showing that in dimension 2 Landsberg condition implies Berwald condition.

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Ricardo Gallego Torrome. 2010-09-22. On the two dimensional Berwald-Landsberg problem. https://doi.org/10.1063/1.3479318

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